/*
 * DoubleSVDDecomp.cs
 * Managed code is a port of JAMA and Jampack code.
 * Copyright (c) 2003-2004, dnAnalytics Project. All rights reserved.
*/

using System;
using dnA.Exceptions;
using System.Runtime.InteropServices;

namespace dnA.Math {
	///<summary>This class computes the SVD factorization of a general <c>DoubleMatrix</c>.</summary>
	public sealed class DoubleSVDDecomp : Algorithm {
		private DoubleMatrix u;
		private DoubleMatrix v;
		private DoubleMatrix w;
		private DoubleMatrix matrix;
		private bool computeVectors;
		
/*		///<summary>Returns the left singular vectors.</summary>
		///<returns>the left singular vectors. The vectors will be <c>null</c> if,
		///computerVectors is set to false.</returns>
		public DoubleMatrix U {
			get{
				Compute();
				return u;
			}
		}

		///<summary>Returns the right singular vectors.</summary>
		///<returns>the right singular vectors. The vectors will be <c>null</c> if,
		///computerVectors is set to false.</returns>
		public DoubleMatrix V{
			get{
				Compute();
				return v;
			}
		}
*/
		///<summary>Returns the singular values as a diagonal matrix.</summary>
		///<returns>the singular values as a diagonal matrix.</returns>
		public DoubleMatrix S {
			get{
				Compute();
				return w;
			}
		}

		///<summary>Returns the two norm of the matrix.</summary>
		///<returns>the two norm of the matrix.</returns>
		public double Norm2{
			get{
				Compute();
				return w[0,0];
			}
		}

		///<summary>Returns the condition number <c>max(S) / min(S)</c>.</summary>
		///<returns>the condition number.</returns>
		public double Condition {
			get{
				Compute();
				int tmp = System.Math.Min(matrix.RowLength,matrix.ColumnLength)-1;
				return w[0,0]/w[tmp,tmp];
			}
		}

		///<summary>Returns the effective numerical matrix rank>.</summary>
		///<returns>the number of nonnegligible singular values.</returns>
		public int Rank{
			get{
				Compute();
				double eps = System.Math.Pow(2.0,-52.0);
				double tol = System.Math.Max(matrix.RowLength,matrix.ColumnLength)*w[0,0]*eps;
				int r = 0;
				for (int i = 0; i < w.RowLength; i++) {
					if (w[i,i] > tol) {
						r++;
					}
				}
				return r;
			}
		}

/*		///<summary>Constructor for SVD decomposition class.</summary>
		///<param name="matrix">The matrix to decompose.</param>
		///<param name="computeVectors">Whether to compute the singular vectors or not.</param>
		///<exception cref="ArgumentNullException">matrix is null.</exception>
		public DoubleSVDDecomp(DoubleMatrix matrix, bool computeVectors){
			if ( matrix == null ) {
				throw new System.ArgumentNullException("matrix cannot be null.");
			}
			this.matrix = matrix.Clone();
			this.computeVectors = computeVectors;
		}
*/
		///<summary>Constructor for SVD decomposition class.</summary>
		///<param name="matrix">The matrix to decompose.</param>
		///<exception cref="ArgumentNullException">matrix is null.</exception>
		public DoubleSVDDecomp(DoubleMatrix matrix){
			if ( matrix == null ) {
				throw new System.ArgumentNullException("matrix cannot be null.");
			}
			this.matrix = matrix.Clone();
			computeVectors = false;
		}
		
		///<summary>Computes the algorithm.</summary>
		protected override void InternalCompute(){
			int m = matrix.RowLength;
			int n = matrix.ColumnLength;
#if MANAGED
			// Derived from LINPACK code.
			// Initialize.
			double[][] A = null;
			double[] s = null;
			int nu = 0;
			if( matrix.RowLength < matrix.ColumnLength ){
				m = matrix.ColumnLength;
				n = matrix.RowLength;
				nu = System.Math.Min(m,n);
				u = new DoubleMatrix(m,nu);
				v = new DoubleMatrix(n);
				s = new double[System.Math.Min(m+1,n)];
				A = matrix.GetTranspose().data;
			}else{
				nu = System.Math.Min(m,n);
				u = new DoubleMatrix(m,nu);
				v = new DoubleMatrix(n);
				s = new double[System.Math.Min(m+1,n)];
				A = new DoubleMatrix(matrix).data;
			}
			double[] e = new double[n];
			double[] work = new double[m];

			// Reduce A to bidiagonal form, storing the diagonal elements
			// in s and the super-diagonal elements in e.

			int nct = System.Math.Min(m-1,n);
			int nrt = System.Math.Max(0,System.Math.Min(n-2,m));
			for (int k = 0; k < System.Math.Max(nct,nrt); k++) {
				if (k < nct) {
					// Compute the transformation for the k-th column and
					// place the k-th diagonal in s[k].
					// Compute 2-norm of k-th column without under/overflow.
					s[k] = 0;
					for (int i = k; i < m; i++) {
						s[k] = Hypotenuse.Compute(s[k],A[i][k]);
					}
					if (s[k] != 0.0) {
						if (A[k][k] < 0.0) {
							s[k] = -s[k];
						}
						for (int i = k; i < m; i++) {
							A[i][k] /= s[k];
						}
						A[k][k] += 1.0;
					}
					s[k] = -s[k];
				}
				for (int j = k+1; j < n; j++) {
					if ((k < nct) & (s[k] != 0.0)) {

						// Apply the transformation.

						double t = 0;
						for (int i = k; i < m; i++) {
							t += A[i][k]*A[i][j];
						}
						t = -t/A[k][k];
						for (int i = k; i < m; i++) {
							A[i][j] += t*A[i][k];
						}
					}

					// Place the k-th row of A into e for the
					// subsequent calculation of the row transformation.

					e[j] = A[k][j];
				}
				if (computeVectors & (k < nct)) {

					// Place the transformation in u.data for subsequent back
					// multiplication.

					for (int i = k; i < m; i++) {
						u.data[i][k] = A[i][k];
					}
				}
				if (k < nrt) {

					// Compute the k-th row transformation and place the
					// k-th super-diagonal in e[k].
					// Compute 2-norm without under/overflow.
					e[k] = 0;
					for (int i = k+1; i < n; i++) {
						e[k] = Hypotenuse.Compute(e[k],e[i]);
					}
					if (e[k] != 0.0) {
						if (e[k+1] < 0.0) {
							e[k] = -e[k];
						}
						for (int i = k+1; i < n; i++) {
							e[i] /= e[k];
						}
						e[k+1] += 1.0;
					}
					e[k] = -e[k];
					if ((k+1 < m) & (e[k] != 0.0)) {

						// Apply the transformation.

						for (int i = k+1; i < m; i++) {
							work[i] = 0.0;
						}
						for (int j = k+1; j < n; j++) {
							for (int i = k+1; i < m; i++) {
								work[i] += e[j]*A[i][j];
							}
						}
						for (int j = k+1; j < n; j++) {
							double t = -e[j]/e[k+1];
							for (int i = k+1; i < m; i++) {
								A[i][j] += t*work[i];
							}
						}
					}
					if (computeVectors) {

						// Place the transformation in v.data for subsequent
						// back multiplication.

						for (int i = k+1; i < n; i++) {
							v.data[i][k] = e[i];
						}
					}
				}
			}

			// Set up the final bidiagonal matrix or order p.

			int p = System.Math.Min(n,m+1);
			if (nct < n) {
				s[nct] = A[nct][nct];
			}
			if (m < p) {
				s[p-1] = 0.0;
			}
			if (nrt+1 < p) {
				e[nrt] = A[nrt][p-1];
			}
			e[p-1] = 0.0;

			// If required, generate u.data.

			if (computeVectors) {
				for (int j = nct; j < nu; j++) {
					for (int i = 0; i < m; i++) {
						u.data[i][j] = 0.0;
					}
					u.data[j][j] = 1.0;
				}
				for (int k = nct-1; k >= 0; k--) {
					if (s[k] != 0.0) {
						for (int j = k+1; j < nu; j++) {
							double t = 0;
							for (int i = k; i < m; i++) {
								t += u.data[i][k]*u.data[i][j];
							}
							t = -t/u.data[k][k];
							for (int i = k; i < m; i++) {
								u.data[i][j] += t*u.data[i][k];
							}
						}
						for (int i = k; i < m; i++ ) {
							u.data[i][k] = -u.data[i][k];
						}
						u.data[k][k] = 1.0 + u.data[k][k];
						for (int i = 0; i < k-1; i++) {
							u.data[i][k] = 0.0;
						}
					} else {
						for (int i = 0; i < m; i++) {
							u.data[i][k] = 0.0;
						}
						u.data[k][k] = 1.0;
					}
				}
			}

			// If required, generate v.data.

			if (computeVectors) {
				for (int k = n-1; k >= 0; k--) {
					if ((k < nrt) & (e[k] != 0.0)) {
						for (int j = k+1; j < nu; j++) {
							double t = 0;
							for (int i = k+1; i < n; i++) {
								t += v.data[i][k]*v.data[i][j];
							}
							t = -t/v.data[k+1][k];
							for (int i = k+1; i < n; i++) {
								v.data[i][j] += t*v.data[i][k];
							}
						}
					}
					for (int i = 0; i < n; i++) {
						v.data[i][k] = 0.0;
					}
					v.data[k][k] = 1.0;
				}
			}

			// Main iteration loop for the singular values.

			int pp = p-1;
			int iter = 0;
			double eps = System.Math.Pow(2.0,-52.0);
			while (p > 0) {
				int k,kase;

				// Here is where a test for too many iterations would go.

				// This section of the program inspects for
				// negligible elements in the s and e arrays.  On
				// completion the variables kase and k are set as follows.

				// kase = 1     if s(p) and e[k-1] are negligible and k<p
				// kase = 2     if s(k) is negligible and k<p
				// kase = 3     if e[k-1] is negligible, k<p, and
				//              s(k), ..., s(p) are not negligible (qr step).
				// kase = 4     if e(p-1) is negligible (convergence).

				for (k = p-2; k >= -1; k--) {
					if (k == -1) {
						break;
					}
					if (System.Math.Abs(e[k]) <= eps*(System.Math.Abs(s[k]) + System.Math.Abs(s[k+1]))) {
						e[k] = 0.0;
						break;
					}
				}
				if (k == p-2) {
					kase = 4;
				} else {
					int ks;
					for (ks = p-1; ks >= k; ks--) {
						if (ks == k) {
							break;
						}
						double t = (ks != p ? System.Math.Abs(e[ks]) : 0.0) + 
							(ks != k+1 ? System.Math.Abs(e[ks-1]) : 0.0);
						if (System.Math.Abs(s[ks]) <= eps*t) {
							s[ks] = 0.0;
							break;
						}
					}
					if (ks == k) {
						kase = 3;
					} else if (ks == p-1) {
						kase = 1;
					} else {
						kase = 2;
						k = ks;
					}
				}
				k++;

				// Perform the task indicated by kase.

				switch (kase) {

						// Deflate negligible s(p).
                
					case 1: {
						double f = e[p-2];
						e[p-2] = 0.0;
						for (int j = p-2; j >= k; j--) {
							double t = Hypotenuse.Compute(s[j],f);
							double cs = s[j]/t;
							double sn = f/t;
							s[j] = t;
							if (j != k) {
								f = -sn*e[j-1];
								e[j-1] = cs*e[j-1];
							}
							if (computeVectors) {
								for (int i = 0; i < n; i++) {
									t = cs*v.data[i][j] + sn*v.data[i][p-1];
									v.data[i][p-1] = -sn*v.data[i][j] + cs*v.data[i][p-1];
									v.data[i][j] = t;
								}
							}
						}
					}
						break;

						// Split at negligible s(k).

					case 2: {
						double f = e[k-1];
						e[k-1] = 0.0;
						for (int j = k; j < p; j++) {
							double t = Hypotenuse.Compute(s[j],f);
							double cs = s[j]/t;
							double sn = f/t;
							s[j] = t;
							f = -sn*e[j];
							e[j] = cs*e[j];
							if (computeVectors) {
								for (int i = 0; i < m; i++) {
									t = cs*u.data[i][j] + sn*u.data[i][k-1];
									u.data[i][k-1] = -sn*u.data[i][j] + cs*u.data[i][k-1];
									u.data[i][j] = t;
								}
							}
						}
					}
						break;

						// Perform one qr step.

					case 3: {

						// Calculate the shift.

						double scale = System.Math.Max(System.Math.Max(System.Math.Max(System.Math.Max(
							System.Math.Abs(s[p-1]),System.Math.Abs(s[p-2])),System.Math.Abs(e[p-2])), 
							System.Math.Abs(s[k])),System.Math.Abs(e[k]));
						double sp = s[p-1]/scale;
						double spm1 = s[p-2]/scale;
						double epm1 = e[p-2]/scale;
						double sk = s[k]/scale;
						double ek = e[k]/scale;
						double b = ((spm1 + sp)*(spm1 - sp) + epm1*epm1)/2.0;
						double c = (sp*epm1)*(sp*epm1);
						double shift = 0.0;
						if ((b != 0.0) | (c != 0.0)) {
							shift = System.Math.Sqrt(b*b + c);
							if (b < 0.0) {
								shift = -shift;
							}
							shift = c/(b + shift);
						}
						double f = (sk + sp)*(sk - sp) + shift;
						double g = sk*ek;

						// Chase zeros.

						for (int j = k; j < p-1; j++) {
							double t = Hypotenuse.Compute(f,g);
							double cs = f/t;
							double sn = g/t;
							if (j != k) {
								e[j-1] = t;
							}
							f = cs*s[j] + sn*e[j];
							e[j] = cs*e[j] - sn*s[j];
							g = sn*s[j+1];
							s[j+1] = cs*s[j+1];
							if (computeVectors) {
								for (int i = 0; i < n; i++) {
									t = cs*v.data[i][j] + sn*v.data[i][j+1];
									v.data[i][j+1] = -sn*v.data[i][j] + cs*v.data[i][j+1];
									v.data[i][j] = t;
								}
							}
							t = Hypotenuse.Compute(f,g);
							cs = f/t;
							sn = g/t;
							s[j] = t;
							f = cs*e[j] + sn*s[j+1];
							s[j+1] = -sn*e[j] + cs*s[j+1];
							g = sn*e[j+1];
							e[j+1] = cs*e[j+1];
							if (computeVectors && (j < m-1)) {
								for (int i = 0; i < m; i++) {
									t = cs*u.data[i][j] + sn*u.data[i][j+1];
									u.data[i][j+1] = -sn*u.data[i][j] + cs*u.data[i][j+1];
									u.data[i][j] = t;
								}
							}
						}
						e[p-2] = f;
						iter = iter + 1;
					}
						break;

						// Convergence.

					case 4: {

						// Make the singular values positive.

						if (s[k] <= 0.0) {
							s[k] = (s[k] < 0.0 ? -s[k] : 0.0);
							if (computeVectors) {
								for (int i = 0; i <= pp; i++) {
									v.data[i][k] = -v.data[i][k];
								}
							}
						}

						// Order the singular values.

						while (k < pp) {
							if (s[k] >= s[k+1]) {
								break;
							}
							double t = s[k];
							s[k] = s[k+1];
							s[k+1] = t;
							if (computeVectors && (k < n-1)) {
								for (int i = 0; i < n; i++) {
									t = v.data[i][k+1]; v.data[i][k+1] = v.data[i][k]; v.data[i][k] = t;
								}
							}
							if (computeVectors && (k < m-1)) {
								for (int i = 0; i < m; i++) {
									t = u.data[i][k+1]; u.data[i][k+1] = u.data[i][k]; u.data[i][k] = t;
								}
							}
							k++;
						}
						iter = 0;
						p--;
					}
						break;
				}
			}
			if(computeVectors && matrix.RowLength < matrix.ColumnLength ){
				DoubleMatrix tmp = u;
				u = v;
				v = new DoubleMatrix(matrix.ColumnLength);
				for( int i = 0; i < matrix.ColumnLength; i++ ){
					for( int j = 0; j < matrix.RowLength; j++ ){
						v[i,j] = tmp[i,j];
					}
				}
			}
#else
			int nu = System.Math.Min(m,n);
			double[] s = new double[System.Math.Min(m+1,n)];
			u = new DoubleMatrix(m,nu);
			v = new DoubleMatrix(n);
			double[] a = new double[matrix.data.Length];
			Array.Copy(matrix.data, a, matrix.data.Length);
			dnA.Math.Lapack.Gesvd.Compute(m, n, a, s, u.data, v.data );
			v.Transpose();
#endif		
			int slen = System.Math.Min(matrix.RowLength,matrix.ColumnLength);
			w = new DoubleMatrix(slen,matrix.ColumnLength);
			for ( int i = 0; i < slen; i++ ) {
				w[i,i] = s[i];
			}
			if( !computeVectors ){
				u = null;
				v = null;
			}
		}
	}
}